In the early 1950's Dirac and Bergmann independently developed the Hamiltonian formalism for systems with singular Lagrangians
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These systems, often called “constrained Hamiltonian systems", include gauge theories. Gauge freedom is more clearly and more completely displayed in the Hamiltonian setting, with the generators of gauge transformations expressed
as functions on phase space. Historically, the main motivation for casting gauge theories in Hamiltonian form was to facilitate their canonical quantization. Dirac and Bergmann were primarily motivated by the prospect of developing a quantum theory of gravity based on a Hamiltonian formulation of general relativity.
